The 360 outputs at 60Hz, yes. No device on the consumer market outputs at a higher rate than this. A few may do something like 96Hz, but that is scaling rather than true frame rate.
I assume you have a 120Hz+ LCD and are wondering why it doesn't say that in the info. The 120Hz+ is done by the TV, interpolating input frames to it's expanded refresh rate capabilities. Seeing 24/30/60Hz in the info bar is perfectly normal and to be expected.
Yeah a lot of TVs LCD and Plasma can be marketed at 120Hz or 240Hz and it's just image processing and can lead to the soap opera effect in games. Most LCD TVs actually refresh at 60Hz and it's not uncommon for Plasma to do 120Hz. I wouldn't worry too much
about burn in on a modern mid-high end plasma set.